Kaustubh

Member • Oct 31, 2008

## Difference between "Not Defined" and "Infinity" [Division by zero]

Okay, let's see if we have confusion about this concept: -

What is the result that you get when you divide a number by zero? Is it "infinity" or is it "not defined"?

Is there any difference between the two?

Or Infinity is not defined? 😁

Update:

Let me try to offer my thoughts on this topic.

In the realm of mathematics and engineering, the notion of dividing by zero is a well-trodden path that leads to undefined territory.

When we delve into the act of division, we're essentially inquiring about the number of times one quantity can be contained within another.

However, when the divisor plunges to zero, the question becomes inherently flawed, thus yielding an undefined result.

Infinity, on the other hand, is a concept that embodies an unbounded quantity. While it's not a real number that we can perform conventional arithmetic with, it's a useful idea in many fields, expressing the notion of a quantity without bound.

Now, when you attempt to divide a non-zero number by zero, some may be tempted to proclaim the result as infinity due to the boundless nature of the division.

However, this is a misstep, as infinity is more of a concept rather than a concrete number. The operation is actually undefined in standard arithmetic.

The confusion often stems from the limit scenario, where we examine the behavior of a function as it approaches a certain point.

For instance, as we divide 1 by a number that approaches zero, the result shoots towards infinity. Yet, this is a journey towards infinity, not a concrete arrival at it.

Thus, in summary, the act of dividing by zero is undefined within the standard arithmetic framework.

Infinity and "undefined" are distinct terms with different implications, and the relationship between them in this context is a reflection of the limit scenario, not a direct equivalence.

So, when faced with division by zero, it's prudent to stick with "undefined" as the rightful descriptor.